This book covers key topics in Galois theory and advanced linear algebra, such as canonical forms and the Cayley–Hamilton theorem. It is structured in four chapters, presenting new theorems and serving as a textbook for undergraduates. A foundational understanding of groups, rings, fields, and vector spaces is recommended.
Focusing on advanced topics in Newtonian rigid dynamics, this textbook covers D'Alembert's principle, virtual work, and Lagrange's equation, among others. It delves into the motion of a top and the momental ellipsoid of a rigid body, emphasizing the conservation principle of angular momentum. With over 350 solved examples and figures, it effectively illustrates complex concepts. Tailored for advanced undergraduate and graduate students in physics, mathematics, and engineering, it provides essential mathematical foundations as needed throughout the text.
Focusing on measure theory and Lebesgue measure, this volume introduces key concepts like the Riesz representation theorem and essential theorems in real and complex analysis. Aimed at undergraduate mathematics and engineering students, it provides a rigorous exploration of exponential and measurable functions, Borel and Lebesgue measures, and the Fubini theorem, among others. The book is structured into three chapters and includes extensive exercises with solutions, making it a comprehensive resource for foundational analysis with minimal prerequisites.
Focusing on holomorphic functions, this volume serves as an accessible introduction to complex analysis for undergraduate mathematics and engineering students. It carefully addresses multivalued functions and employs complex measures and power series. The text is organized into four chapters covering key concepts like the Schwarz reflection principle, Riemann mapping theorem, and analytic continuation, among others. It also features extensive exercises with solutions, reinforcing the material while highlighting significant theorems from renowned mathematicians of the 19th and 20th centuries.
Focusing on the theory of smooth manifolds, this book serves as a comprehensive introduction for graduate students and researchers in mathematics. It covers essential topics such as differential manifolds, tangent spaces, and key theorems like Sard's and Whitney's. The clear structure, numerous illustrations, and solved examples enhance understanding, while complex theorems are broken down into manageable lemmas. Concepts are revisited throughout to reinforce learning, making it accessible even to undergraduates. The emphasis on mathematical proofs highlights the joy of discovery in mathematics.